.7x+.1x(.7+x)=30

Solution for .7x+.1x(.7+x)=30 equation:

.7x+.1x(.7+x)=30

We move all terms to the left:

.7x+.1x(.7+x)-(30)=0

We add all the numbers together, and all the variables

.7x+.1x(x+0.7)-30=0

We multiply parentheses

x^2+.7x+0.7x-30=0

We add all the numbers together, and all the variables

x^2+1.4x-30=0

a = 1; b = 1.4; c = -30;
Δ = b2-4ac
Δ = 1.42-4·1·(-30)
Δ = 121.96
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1.4)-\sqrt{121.96}}{2*1}=\frac{-1.4-\sqrt{121.96}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.4)+\sqrt{121.96}}{2*1}=\frac{-1.4+\sqrt{121.96}}{2}
$